MOTA 31POWERS AND POLYNOMIALS 139 96. (a) Use the formula for the area of a circle of radius r A nr2, to find dA/dr. (b) The result from part (a) should look familiar. What does d A/dr represent geometrically? L(c) Use the difference quotient to explain the observa- tion you made in part (b). 97. Show that for any power function f(x) = x", we have f'(1) n. 98. Suppose W is proportional to r. The derivative d/dr is proportional to what power of ? 99. Given a power function of the form f(x) = ax", with f'(2)= 3 and f'(4) = 24, findn and a. 100. (a) Find the value of a making f(x) continuous at 11 x= 1:

Q: find GA

A: Given figure:-

Q: 2. Construct a boxplot. 1, 2, 2, 3, 3, 4, 5, 6, 7, 7, 8, 8, 8, 9, 10, 11, 11, 13, 15, 15, 21, 24,…

A:

Q: 3,5,12,55,648?

A: If we see this pattern clearly we can see  3,5,12,55,648 3*5-3 = 12 5*12-5 = 55 12*55-12 = 648 So…

Q: 12, 18, 23, 14, 14, 16, 20, 16, 14, 16 O

A: Given that, 12, 18, 23, 14, 14, 16, 20, 16, 14, 16

Q: 4) 45

A: The length of the side AB=32 units. An angle m∠A=45∘ The objective is to find the value of 'x'.

Q: 4.3

A:

Q: Find the Rank of A 3. A = 4

A: Here we have to find the rank of the matrix A=413413413

Q: 7) 6,062

A:

Q: Find the sixth term of the G.P. 6, 2,..

A: Given first two terms of a geometric progression series,  6,2,... To find the sixth term of the…

Q: 9:4=_:32

A:

Q: 28)9,589

A: Given

Q: 7 to the power of 18

A: To determine: 7 to the power of 18

Q: 6, 1, –4, –9, ...

A:

Q: Estimate v83 to the nearest (a) integer and (b) tenth. a. V83 b. V83

A:

Q: Trying to answer c)

A: Refer Standard normal table/Z-table, Lookup for z-score corresponding to area 0.10 to the left of…

Q: 2. Find a2ı for {121, 118, 115, . . .}

A: 2. The arithmetic sequence is given by 121, 118, 115,........ Formula Used : an = a1+n-1d…

Q: 2. Find x in AABC. 16

A:

Q: 43,716 19,537

A:

Q: 189 2,834 696 2,834

A: We flip the denominator and multiply with the numerator.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.